The Lehmer lengths of the generalized quaternion group Q2n

2017 ◽  
Author(s):  
Ömür Deveci ◽  
Abdulkadir Kalemci
Keyword(s):  
Quaternion Group ◽  
Generalized Quaternion Group ◽  
Generalized Quaternion

scholarly journals Corrigenda On a classification of the function fields of algebraic tori: (Nagoya Math. J. 56 (1975), 85–104)

1980 ◽  
Vol 79 ◽  
pp. 187-190 ◽  
Author(s):  
Shizuo Endo ◽  
Takehiko Miyata
Keyword(s):  
Direct Product ◽  
Cyclic Group ◽  
Prime Divisor ◽  
Dihedral Group ◽  
Quaternion Group ◽  
Algebraic Tori ◽  
Root Of Unity ◽  
Generalized Quaternion Group ◽  
Generalized Quaternion

There are some errors in Theorems 3.3 and 4.2 in [2]. In this note we would like to correct them.1) In Theorem 3.3 (and [IV]), the condition (1) must be replaced by the following one;(1) П is (i) a cyclic group, (ii) a dihedral group of order 2m, m odd, (iii) a direct product of a cyclic group of order qf, q an odd prime, f ≧ 1, and a dihedral group of order 2m, m odd, where each prime divisor of m is a primitive qf-1(q — 1)-th root of unity modulo qf, or (iv) a generalized quaternion group of order 4m, m odd, where each prime divisor of m is congruent to 3 modulo 4.

scholarly journals Embedding Obstructions for the Generalized Quaternion Group

2000 ◽  
Vol 226 (1) ◽  
pp. 375-389 ◽  
Author(s):  
Ivo M. Michailov ◽  
Nikola P. Ziapkov
Keyword(s):  
Quaternion Group ◽  
Generalized Quaternion Group ◽  
Generalized Quaternion

On the Structure of Augmentation Quotient Groups for the Generalized Quaternion Group

2012 ◽  
Vol 19 (01) ◽  
pp. 137-148 ◽  
Author(s):  
Qingxia Zhou ◽  
Hong You
Keyword(s):  
Group Ring ◽  
Integral Group Ring ◽  
Augmentation Ideal ◽  
Integral Group ◽  
Quaternion Group ◽  
Generalized Quaternion Group ◽  
Augmentation Quotient ◽  
Generalized Quaternion ◽  
Quotient Groups

For the generalized quaternion group G, this article deals with the problem of presenting the nth power Δn(G) of the augmentation ideal Δ (G) of the integral group ring ZG. The structure of Qn(G)=Δn(G)/Δn+1(G) is obtained.

SYMMETRY CLASSES OF POLYNOMIALS ASSOCIATED WITH THE DICYCLIC GROUP

2013 ◽  
Vol 06 (03) ◽  
pp. 1350033 ◽  
Author(s):  
Yousef Zamani ◽  
Esmaeil Babaei
Keyword(s):  
Symmetric Group ◽  
Quaternion Group ◽  
Irreducible Characters ◽  
Symmetry Classes ◽  
Generalized Quaternion Group ◽  
Generalized Quaternion

In this paper, we obtain the dimensions of symmetry classes of polynomials with respect to the irreducible characters of the dicyclic group as a subgroup of the full symmetric group. Then we discuss the existence of o-basis of these classes. In particular, the existence of o-basis of symmetry classes of polynomials with respect to the irreducible characters of the generalized quaternion group are concluded.

scholarly journals Finite nilpotent groups that coincide with their 2-closures in all of their faithful permutation representations

2018 ◽  
Vol 17 (04) ◽  
pp. 1850065
Author(s):  
Alireza Abdollahi ◽  
Majid Arezoomand
Keyword(s):  
Nilpotent Group ◽  
Direct Product ◽  
Cyclic Group ◽  
Nilpotent Groups ◽  
Quaternion Group ◽  
Finite Nilpotent Group ◽  
Closed Group ◽  
Odd Order ◽  
Generalized Quaternion Group ◽  
Generalized Quaternion

Let [Formula: see text] be any group and [Formula: see text] be a subgroup of [Formula: see text] for some set [Formula: see text]. The [Formula: see text]-closure of [Formula: see text] on [Formula: see text], denoted by [Formula: see text], is by definition, [Formula: see text] The group [Formula: see text] is called [Formula: see text]-closed on [Formula: see text] if [Formula: see text]. We say that a group [Formula: see text] is a totally[Formula: see text]-closed group if [Formula: see text] for any set [Formula: see text] such that [Formula: see text]. Here we show that the center of any finite totally 2-closed group is cyclic and a finite nilpotent group is totally 2-closed if and only if it is cyclic or a direct product of a generalized quaternion group with a cyclic group of odd order.

scholarly journals Hurwitz Equivalence in Tuples of Generalized Quaternion Groups and Dihedral Groups

10.37236/804 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Xiang-dong Hou
Keyword(s):  
Dihedral Group ◽  
Quaternion Group ◽  
Dihedral Groups ◽  
Generalized Quaternion Group ◽  
Hurwitz Action ◽  
Generalized Quaternion

Let $Q_{2^m}$ be the generalized quaternion group of order $2^m$ and $D_N$ the dihedral group of order $2N$. We classify the orbits in $Q_{2^m}^n$ and $D_{p^m}^n$ ($p$ prime) under the Hurwitz action.

The digraphs arising by the power maps of generalized quaternion groups

2016 ◽  
Vol 16 (09) ◽  
pp. 1750179 ◽  
Author(s):  
Uzma Ahmad ◽  
Muqadas Moeen
Keyword(s):  
Natural Number ◽  
Quaternion Group ◽  
Power Maps ◽  
Generalized Quaternion Group ◽  
Number Of Cycles ◽  
Generalized Quaternion

We attach a diagraph with generalized Quaternion group of order [Formula: see text] by utilizing the power map [Formula: see text] defined by [Formula: see text] for all [Formula: see text], where [Formula: see text] is a fixed natural number. We examine the structure of these power digraphs and establish numerous results encapsulating the existence of cycle vertices, derivation of different formulae concerning the number of cycles, length of cycles and most importantly in-degree of vertices. Moreover, we categorize the regular and semi-regular power digraphs.

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